The recently predicted ZrB₄ with an Amm2 orthorhombic structure has great scientific and technical significance owing to its novel B–Zr–B “sandwich” layer bonding and evaluated high hardness. To better understand the performance of Amm2-ZrB₄, its elastic and thermodynamic properties under pressure and temperature are studied here by taking advantage of first principles calculations in combination with the quasi-harmonic Debye model. It is found that ZrB₄ keeps brittleness and mechanical stability up to 100 GPa, possessing pronounced elastic anisotropy demonstrated by the elastic anisotropy factors, the direction-dependent Young's modulus, shear modulus and Poisson's ratio. The pressure and temperature dependences of the thermodynamics parameters including normalized volume V/V₀, bulk modulus, specific heat, Debye temperature, thermal expansion coefficient and Grüneisen parameter in wide temperature (0–1000 K) and pressure (0–50 GPa) ranges are obtained and discussed in detail.